Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [880,2,Mod(17,880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(880, base_ring=CyclotomicField(20))
chi = DirichletCharacter(H, H._module([0, 0, 5, 18]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("880.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 880 = 2^{4} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 880.cm (of order \(20\), degree \(8\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.02683537787\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{20})\) |
Twist minimal: | no (minimal twist has level 220) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{20}]$ |
Embedding invariants
Embedding label | 17.5 | ||
Character | \(\chi\) | \(=\) | 880.17 |
Dual form | 880.2.cm.b.673.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/880\mathbb{Z}\right)^\times\).
\(n\) | \(111\) | \(177\) | \(321\) | \(661\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.834729 | − | 0.132208i | 0.481931 | − | 0.0763304i | 0.0892580 | − | 0.996009i | \(-0.471550\pi\) |
0.392673 | + | 0.919678i | \(0.371550\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.08639 | + | 0.804354i | −0.933061 | + | 0.359718i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.228981 | − | 1.44573i | 0.0865468 | − | 0.546435i | −0.905874 | − | 0.423548i | \(-0.860785\pi\) |
0.992421 | − | 0.122887i | \(-0.0392154\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.17388 | + | 0.706335i | −0.724625 | + | 0.235445i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.21121 | − | 0.829518i | 0.968218 | − | 0.250109i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.134489 | − | 0.263950i | 0.0373006 | − | 0.0732065i | −0.871604 | − | 0.490211i | \(-0.836920\pi\) |
0.908905 | + | 0.417004i | \(0.136920\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.63523 | + | 0.947255i | −0.422214 | + | 0.244580i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.43144 | + | 6.73459i | 0.832247 | + | 1.63338i | 0.772371 | + | 0.635172i | \(0.219071\pi\) |
0.0598764 | + | 0.998206i | \(0.480929\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.63943 | + | 3.37075i | 1.06436 | + | 0.773302i | 0.974890 | − | 0.222688i | \(-0.0714830\pi\) |
0.0894690 | + | 0.995990i | \(0.471483\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 1.23707i | − | 0.269950i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.96043 | − | 5.96043i | 1.24284 | − | 1.24284i | 0.284017 | − | 0.958819i | \(-0.408333\pi\) |
0.958819 | − | 0.284017i | \(-0.0916673\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.70603 | − | 3.35639i | 0.741206 | − | 0.671278i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.98027 | + | 2.02805i | −0.766004 | + | 0.390299i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.71592 | − | 4.87940i | 1.24711 | − | 0.906081i | 0.249063 | − | 0.968487i | \(-0.419877\pi\) |
0.998051 | + | 0.0624057i | \(0.0198773\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.792277 | + | 2.43838i | 0.142297 | + | 0.437946i | 0.996654 | − | 0.0817419i | \(-0.0260483\pi\) |
−0.854356 | + | 0.519688i | \(0.826048\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.57083 | − | 1.11697i | 0.447523 | − | 0.194440i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.685136 | + | 3.20054i | 0.115809 | + | 0.540990i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.12739 | + | 0.336946i | 0.349741 | + | 0.0553935i | 0.328834 | − | 0.944388i | \(-0.393344\pi\) |
0.0209075 | + | 0.999781i | \(0.493344\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.0773657 | − | 0.238107i | 0.0123884 | − | 0.0381277i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.70705 | + | 6.47870i | −0.735117 | + | 1.01180i | 0.263767 | + | 0.964586i | \(0.415035\pi\) |
−0.998885 | + | 0.0472159i | \(0.984965\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.62512 | − | 2.62512i | −0.400327 | − | 0.400327i | 0.478021 | − | 0.878348i | \(-0.341354\pi\) |
−0.878348 | + | 0.478021i | \(0.841354\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.96741 | − | 3.22225i | 0.591426 | − | 0.480345i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.04991 | + | 6.62887i | 0.153145 | + | 0.966919i | 0.937848 | + | 0.347047i | \(0.112816\pi\) |
−0.784703 | + | 0.619872i | \(0.787184\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.61969 | + | 1.50103i | 0.659956 | + | 0.214433i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.75469 | + | 5.16789i | 0.525762 | + | 0.723650i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.739201 | + | 0.376642i | 0.101537 | + | 0.0517357i | 0.504021 | − | 0.863691i | \(-0.331853\pi\) |
−0.402484 | + | 0.915427i | \(0.631853\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.03261 | + | 4.31365i | −0.813437 | + | 0.581653i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.31831 | + | 2.20029i | 0.571974 | + | 0.291435i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.495669 | + | 0.682230i | 0.0645306 | + | 0.0888188i | 0.840062 | − | 0.542490i | \(-0.182518\pi\) |
−0.775532 | + | 0.631308i | \(0.782518\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.88340 | − | 1.26179i | −0.497219 | − | 0.161556i | 0.0496630 | − | 0.998766i | \(-0.484185\pi\) |
−0.546882 | + | 0.837210i | \(0.684185\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.523394 | + | 3.30458i | 0.0659414 | + | 0.416338i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.0682875 | + | 0.658879i | −0.00847002 | + | 0.0817239i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.77012 | − | 8.77012i | −1.07144 | − | 1.07144i | −0.997244 | − | 0.0741974i | \(-0.976361\pi\) |
−0.0741974 | − | 0.997244i | \(-0.523639\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.18733 | − | 5.76336i | 0.504095 | − | 0.693828i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.44164 | − | 4.43691i | 0.171091 | − | 0.526564i | −0.828342 | − | 0.560222i | \(-0.810716\pi\) |
0.999433 | + | 0.0336583i | \(0.0107158\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.17085 | − | 0.660597i | −0.488161 | − | 0.0773171i | −0.0924979 | − | 0.995713i | \(-0.529485\pi\) |
−0.395663 | + | 0.918396i | \(0.629485\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.64979 | − | 3.29164i | 0.305971 | − | 0.380086i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.463953 | − | 4.83250i | −0.0528723 | − | 0.550714i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.875685 | + | 2.69508i | 0.0985223 | + | 0.303220i | 0.988156 | − | 0.153455i | \(-0.0490401\pi\) |
−0.889633 | + | 0.456676i | \(0.849040\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.49330 | − | 1.81149i | 0.277034 | − | 0.201277i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.19653 | − | 4.68587i | 1.00945 | − | 0.514341i | 0.130599 | − | 0.991435i | \(-0.458310\pi\) |
0.878852 | + | 0.477095i | \(0.158310\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.5763 | − | 11.2909i | −1.36409 | − | 1.22467i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.96087 | − | 4.96087i | 0.531861 | − | 0.531861i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.6361i | 1.65742i | 0.559679 | + | 0.828710i | \(0.310925\pi\) | ||||
−0.559679 | + | 0.828710i | \(0.689075\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.350805 | − | 0.254875i | −0.0367744 | − | 0.0267181i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.983710 | + | 1.93064i | 0.102006 | + | 0.200198i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −12.3909 | − | 3.30094i | −1.27128 | − | 0.338669i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.85719 | + | 7.57015i | −0.391638 | + | 0.768633i | −0.999681 | − | 0.0252716i | \(-0.991955\pi\) |
0.608043 | + | 0.793904i | \(0.291955\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.39486 | + | 4.07146i | −0.642708 | + | 0.409198i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.93782 | + | 1.60440i | −0.491332 | + | 0.159643i | −0.544196 | − | 0.838958i | \(-0.683165\pi\) |
0.0528640 | + | 0.998602i | \(0.483165\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.834326 | − | 5.26773i | 0.0822086 | − | 0.519045i | −0.911879 | − | 0.410460i | \(-0.865368\pi\) |
0.994087 | − | 0.108585i | \(-0.0346319\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.995040 | + | 2.58100i | 0.0971059 | + | 0.251880i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.4152 | − | 1.96637i | 1.20022 | − | 0.190096i | 0.475861 | − | 0.879521i | \(-0.342137\pi\) |
0.724357 | + | 0.689425i | \(0.242137\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.5097 | −1.58134 | −0.790671 | − | 0.612241i | \(-0.790268\pi\) | ||||
−0.790671 | + | 0.612241i | \(0.790268\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.82034 | 0.172779 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.69327 | − | 0.584956i | 0.347433 | − | 0.0550280i | 0.0197209 | − | 0.999806i | \(-0.493722\pi\) |
0.327713 | + | 0.944777i | \(0.393722\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.64148 | + | 17.2301i | −0.712572 | + | 1.60671i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.105926 | + | 0.668789i | −0.00979284 | + | 0.0618295i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.5221 | − | 3.41885i | 0.964563 | − | 0.313405i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.62380 | − | 5.32752i | 0.874891 | − | 0.484320i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.07257 | + | 6.03027i | −0.277045 | + | 0.543731i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.03249 | + | 9.98369i | −0.450120 | + | 0.892968i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.78852 | − | 7.43539i | −0.336177 | − | 0.659784i | 0.659598 | − | 0.751619i | \(-0.270727\pi\) |
−0.995774 | + | 0.0918351i | \(0.970727\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.53832 | − | 1.84420i | −0.223487 | − | 0.162373i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 10.5791i | − | 0.924303i | −0.886801 | − | 0.462151i | \(-0.847078\pi\) | ||
0.886801 | − | 0.462151i | \(-0.152922\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.93553 | − | 5.93553i | 0.514676 | − | 0.514676i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.67313 | − | 7.43285i | 0.574331 | − | 0.639718i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.7094 | − | 5.45669i | 0.914962 | − | 0.466197i | 0.0679012 | − | 0.997692i | \(-0.478370\pi\) |
0.847061 | + | 0.531495i | \(0.178370\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.611911 | + | 0.444579i | −0.0519016 | + | 0.0377087i | −0.613434 | − | 0.789746i | \(-0.710212\pi\) |
0.561532 | + | 0.827455i | \(0.310212\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.75278 | + | 5.39450i | 0.147611 | + | 0.454299i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.212922 | − | 0.959161i | 0.0178055 | − | 0.0802091i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.0872 | + | 15.5823i | −0.837700 | + | 1.29404i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.05464 | + | 0.642192i | 0.334421 | + | 0.0529671i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.14368 | − | 3.51989i | 0.0936941 | − | 0.288361i | −0.893217 | − | 0.449626i | \(-0.851557\pi\) |
0.986911 | + | 0.161265i | \(0.0515573\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.43710 | + | 3.35439i | −0.198329 | + | 0.272976i | −0.896585 | − | 0.442872i | \(-0.853960\pi\) |
0.698256 | + | 0.715848i | \(0.253960\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −12.2164 | − | 12.2164i | −0.987638 | − | 0.987638i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.61432 | − | 4.45013i | −0.290309 | − | 0.357443i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.60690 | − | 10.1456i | −0.128245 | − | 0.809705i | −0.965023 | − | 0.262164i | \(-0.915564\pi\) |
0.836779 | − | 0.547541i | \(-0.184436\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.666828 | + | 0.216665i | 0.0528829 | + | 0.0171827i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.25236 | − | 9.98201i | −0.571566 | − | 0.786693i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.87784 | − | 4.01396i | −0.617040 | − | 0.314397i | 0.117386 | − | 0.993086i | \(-0.462548\pi\) |
−0.734426 | + | 0.678689i | \(0.762548\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.46530 | + | 4.39829i | −0.347623 | + | 0.342406i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.28987 | + | 4.22390i | 0.641489 | + | 0.326855i | 0.744300 | − | 0.667846i | \(-0.232783\pi\) |
−0.102810 | + | 0.994701i | \(0.532783\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.58963 | + | 10.4462i | 0.583817 | + | 0.803556i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.4664 | − | 4.05059i | −0.953331 | − | 0.309756i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.309951 | − | 1.95696i | −0.0235652 | − | 0.148785i | 0.973100 | − | 0.230382i | \(-0.0739977\pi\) |
−0.996665 | + | 0.0815978i | \(0.973998\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.00382 | − | 6.12647i | −0.302661 | − | 0.463118i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.503946 | + | 0.503946i | 0.0378789 | + | 0.0378789i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.88852 | + | 6.72847i | −0.365385 | + | 0.502909i | −0.951639 | − | 0.307218i | \(-0.900602\pi\) |
0.586254 | + | 0.810127i | \(0.300602\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.98312 | + | 12.2588i | −0.296063 | + | 0.911187i | 0.686800 | + | 0.726847i | \(0.259015\pi\) |
−0.982862 | + | 0.184341i | \(0.940985\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.40841 | − | 0.539839i | −0.251957 | − | 0.0399060i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.70959 | + | 1.00818i | −0.346256 | + | 0.0741226i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.6056 | + | 18.7798i | 1.21432 | + | 1.37331i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.02061 | + | 6.21879i | 0.146978 | + | 0.452350i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.5051 | + | 13.4447i | −1.33898 | + | 0.972825i | −0.339498 | + | 0.940607i | \(0.610257\pi\) |
−0.999481 | + | 0.0322180i | \(0.989743\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.51445 | + | 0.771651i | −0.109013 | + | 0.0555447i | −0.507647 | − | 0.861565i | \(-0.669484\pi\) |
0.398634 | + | 0.917110i | \(0.369484\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.0301076 | + | 0.559013i | 0.00215605 | + | 0.0400318i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.6799 | − | 10.6799i | 0.760909 | − | 0.760909i | −0.215577 | − | 0.976487i | \(-0.569163\pi\) |
0.976487 | + | 0.215577i | \(0.0691634\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.08438i | 0.573086i | 0.958067 | + | 0.286543i | \(0.0925062\pi\) | ||||
−0.958067 | + | 0.286543i | \(0.907494\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.48016 | − | 6.16119i | −0.598144 | − | 0.434577i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.51648 | − | 10.8267i | −0.387181 | − | 0.759885i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.60956 | − | 17.3032i | 0.321946 | − | 1.20851i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.74718 | + | 17.1673i | −0.607971 | + | 1.19321i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 17.6943 | + | 6.97569i | 1.22394 | + | 0.482519i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.8288 | + | 6.11786i | −1.29623 | + | 0.421171i | −0.874268 | − | 0.485443i | \(-0.838658\pi\) |
−0.421962 | + | 0.906614i | \(0.638658\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.616782 | − | 3.89421i | 0.0422612 | − | 0.266827i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.58854 | + | 3.36549i | 0.517534 | + | 0.229525i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.70666 | − | 0.587077i | 0.251624 | − | 0.0398534i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.56886 | −0.241162 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.23909 | 0.150617 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.2342 | + | 3.67994i | −1.55588 | + | 0.246427i | −0.874325 | − | 0.485341i | \(-0.838696\pi\) |
−0.681554 | + | 0.731768i | \(0.738696\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.68571 | + | 9.91407i | −0.379048 | + | 0.660938i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.82607 | − | 17.8431i | 0.187573 | − | 1.18429i | −0.696715 | − | 0.717348i | \(-0.745356\pi\) |
0.884288 | − | 0.466941i | \(-0.154644\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.957093 | + | 0.310978i | −0.0632465 | + | 0.0205500i | −0.340469 | − | 0.940256i | \(-0.610586\pi\) |
0.277223 | + | 0.960806i | \(0.410586\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.02617 | − | 3.97249i | −0.0675170 | − | 0.261370i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.59481 | − | 5.09261i | 0.169992 | − | 0.333628i | −0.790256 | − | 0.612777i | \(-0.790052\pi\) |
0.960248 | + | 0.279149i | \(0.0900524\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.52247 | − | 12.9859i | −0.490712 | − | 0.847106i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.08727 | + | 2.13389i | 0.0706259 | + | 0.138611i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.3661 | + | 8.25792i | 0.735209 | + | 0.534161i | 0.891207 | − | 0.453597i | \(-0.149859\pi\) |
−0.155998 | + | 0.987757i | \(0.549859\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 16.9893i | − | 1.09438i | −0.837010 | − | 0.547188i | \(-0.815698\pi\) | ||
0.837010 | − | 0.547188i | \(-0.184302\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.3180 | − | 11.3180i | 0.726052 | − | 0.726052i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10.8458 | + | 0.584138i | −0.692914 | + | 0.0373192i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.51366 | − | 0.771249i | 0.0963120 | − | 0.0490734i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.05710 | − | 5.12729i | 0.447226 | − | 0.324929i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.854534 | + | 2.62998i | 0.0539377 | + | 0.166003i | 0.974397 | − | 0.224836i | \(-0.0721848\pi\) |
−0.920459 | + | 0.390839i | \(0.872185\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.1959 | − | 24.0845i | 0.892491 | − | 1.51418i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −11.9906 | − | 7.76212i | −0.750878 | − | 0.486083i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −17.4350 | − | 2.76143i | −1.08756 | − | 0.172253i | −0.413191 | − | 0.910644i | \(-0.635586\pi\) |
−0.674372 | + | 0.738391i | \(0.735586\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.974266 | − | 2.99848i | 0.0605379 | − | 0.186317i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.1531 | + | 15.3509i | −0.690358 | + | 0.950196i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.88362 | − | 2.88362i | −0.177812 | − | 0.177812i | 0.612590 | − | 0.790401i | \(-0.290128\pi\) |
−0.790401 | + | 0.612590i | \(0.790128\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.84521 | − | 0.191242i | −0.113351 | − | 0.0117479i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.06721 | + | 13.0519i | 0.126511 | + | 0.798762i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.43670 | − | 0.791731i | −0.148568 | − | 0.0482727i | 0.233789 | − | 0.972287i | \(-0.424888\pi\) |
−0.382357 | + | 0.924015i | \(0.624888\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.284253 | − | 0.391241i | −0.0172672 | − | 0.0237662i | 0.800296 | − | 0.599605i | \(-0.204676\pi\) |
−0.817563 | + | 0.575839i | \(0.804676\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.326524 | − | 0.166372i | −0.0197621 | − | 0.0100693i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.11667 | − | 13.8523i | 0.549756 | − | 0.835325i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.7580 | − | 10.5767i | −1.24723 | − | 0.635495i | −0.299355 | − | 0.954142i | \(-0.596772\pi\) |
−0.947873 | + | 0.318647i | \(0.896772\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.44463 | − | 4.74112i | −0.206224 | − | 0.283843i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.0251 | + | 5.53180i | 1.01563 | + | 0.329999i | 0.769095 | − | 0.639134i | \(-0.220707\pi\) |
0.246538 | + | 0.969133i | \(0.420707\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.93981 | − | 18.5612i | −0.174753 | − | 1.10335i | −0.906634 | − | 0.421917i | \(-0.861357\pi\) |
0.731881 | − | 0.681433i | \(-0.238643\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −10.7795 | − | 1.11721i | −0.638521 | − | 0.0661776i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.28862 | + | 8.28862i | 0.489262 | + | 0.489262i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −23.5875 | + | 32.4654i | −1.38750 | + | 1.90973i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.21887 | + | 6.82898i | −0.130072 | + | 0.400322i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −26.1531 | − | 4.14224i | −1.52788 | − | 0.241992i | −0.664785 | − | 0.747035i | \(-0.731477\pi\) |
−0.863094 | + | 0.505043i | \(0.831477\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.58291 | − | 1.02470i | −0.0921607 | − | 0.0596605i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −11.0992 | + | 9.81422i | −0.644041 | + | 0.569479i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.771642 | − | 2.37487i | −0.0446252 | − | 0.137342i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.39632 | + | 3.19411i | −0.253400 | + | 0.184106i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.90963 | + | 1.99206i | −0.224602 | + | 0.114441i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.11721 | − | 0.491038i | 0.522050 | − | 0.0281168i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.1395 | − | 10.1395i | 0.578689 | − | 0.578689i | −0.355853 | − | 0.934542i | \(-0.615810\pi\) |
0.934542 | + | 0.355853i | \(0.115810\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 4.50743i | − | 0.256419i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.0796 | − | 14.5887i | −1.13861 | − | 0.827250i | −0.151686 | − | 0.988429i | \(-0.548470\pi\) |
−0.986925 | + | 0.161179i | \(0.948470\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.06879 | − | 2.09761i | −0.0604114 | − | 0.118564i | 0.858827 | − | 0.512267i | \(-0.171194\pi\) |
−0.919238 | + | 0.393703i | \(0.871194\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.75005 | − | 6.47364i | −0.211291 | − | 0.364748i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.30316 | − | 16.2959i | 0.466352 | − | 0.915268i | −0.531326 | − | 0.847167i | \(-0.678306\pi\) |
0.997678 | − | 0.0681004i | \(-0.0216938\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17.5187 | − | 21.2398i | 0.980859 | − | 1.18920i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.1033 | − | 3.28277i | 0.563912 | − | 0.183226i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.78063 | + | 42.8112i | −0.377284 | + | 2.38208i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.387498 | − | 1.42960i | −0.0214945 | − | 0.0793002i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −13.7811 | + | 2.18272i | −0.762098 | + | 0.120704i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.82397 | 0.541613 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.6793 | 0.751883 | 0.375942 | − | 0.926643i | \(-0.377319\pi\) | ||||
0.375942 | + | 0.926643i | \(0.377319\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.86268 | + | 0.770173i | −0.266473 | + | 0.0422052i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 25.3522 | + | 11.2436i | 1.38514 | + | 0.614303i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.94300 | + | 31.2089i | −0.269262 | + | 1.70005i | 0.368342 | + | 0.929690i | \(0.379926\pi\) |
−0.637604 | + | 0.770364i | \(0.720074\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.00554 | − | 0.976560i | 0.163239 | − | 0.0530395i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.56685 | + | 7.17295i | 0.247309 | + | 0.388437i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.87961 | − | 15.4646i | 0.425459 | − | 0.835010i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.10061 | + | 15.3927i | −0.220769 | + | 0.828716i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.84815 | − | 15.4029i | −0.421311 | − | 0.826869i | −0.999936 | − | 0.0112757i | \(-0.996411\pi\) |
0.578626 | − | 0.815593i | \(-0.303589\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.47829 | + | 1.80059i | 0.132660 | + | 0.0963831i | 0.652136 | − | 0.758102i | \(-0.273873\pi\) |
−0.519476 | + | 0.854485i | \(0.673873\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.32334i | 0.0706349i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.1192 | − | 15.1192i | 0.804713 | − | 0.804713i | −0.179115 | − | 0.983828i | \(-0.557323\pi\) |
0.983828 | + | 0.179115i | \(0.0573235\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.561026 | + | 10.4167i | 0.0297762 | + | 0.552861i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.33113 | − | 4.24493i | 0.440930 | − | 0.224665i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.61052 | + | 6.25591i | −0.454446 | + | 0.330174i | −0.791349 | − | 0.611365i | \(-0.790621\pi\) |
0.336903 | + | 0.941540i | \(0.390621\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.29109 | + | 13.2066i | 0.225847 | + | 0.695085i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.32892 | − | 5.71938i | 0.384669 | − | 0.300190i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.23336 | − | 1.97658i | 0.483296 | − | 0.103459i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.3687 | + | 2.90931i | 0.958836 | + | 0.151865i | 0.616188 | − | 0.787599i | \(-0.288676\pi\) |
0.342648 | + | 0.939464i | \(0.388676\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.65641 | − | 17.4086i | 0.294461 | − | 0.906257i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.713786 | − | 0.982442i | 0.0370579 | − | 0.0510058i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.7161 | + | 20.7161i | 1.07264 | + | 1.07264i | 0.997146 | + | 0.0754909i | \(0.0240524\pi\) |
0.0754909 | + | 0.997146i | \(0.475948\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.88084 | + | 8.99901i | −0.148766 | + | 0.464707i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.384699 | − | 2.42889i | −0.0198130 | − | 0.125094i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.95463 | + | 2.58462i | 0.408602 | + | 0.132763i | 0.506104 | − | 0.862473i | \(-0.331085\pi\) |
−0.0975021 | + | 0.995235i | \(0.531085\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.14541 | − | 5.70566i | −0.212376 | − | 0.292310i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 27.9347 | + | 14.2335i | 1.42740 | + | 0.727296i | 0.985485 | − | 0.169762i | \(-0.0543000\pi\) |
0.441913 | + | 0.897058i | \(0.354300\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.85502 | + | 9.70928i | 0.247435 | + | 0.494831i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.56090 | + | 3.85247i | 0.384342 | + | 0.195832i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.58343 | − | 4.93217i | −0.181687 | − | 0.250071i | 0.708453 | − | 0.705758i | \(-0.249394\pi\) |
−0.890140 | + | 0.455687i | \(0.849394\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 60.5940 | + | 19.6882i | 3.06437 | + | 0.995674i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.39865 | − | 8.83071i | −0.0705524 | − | 0.445450i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.99482 | − | 4.91863i | −0.201001 | − | 0.247483i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.9635 | + | 15.9635i | 0.801183 | + | 0.801183i | 0.983281 | − | 0.182097i | \(-0.0582886\pi\) |
−0.182097 | + | 0.983281i | \(0.558289\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.16984 | − | 5.73929i | 0.208753 | − | 0.287324i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.25493 | + | 19.2507i | −0.312356 | + | 0.961334i | 0.664472 | + | 0.747313i | \(0.268656\pi\) |
−0.976829 | + | 0.214022i | \(0.931344\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.750163 | + | 0.118814i | 0.0373683 | + | 0.00591855i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.74492 | + | 5.78497i | −0.186086 | + | 0.287457i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.11101 | − | 0.682706i | 0.352480 | − | 0.0338405i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.33157 | − | 7.17585i | −0.115289 | − | 0.354823i | 0.876718 | − | 0.481004i | \(-0.159728\pi\) |
−0.992007 | + | 0.126181i | \(0.959728\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.21799 | − | 5.97072i | 0.405364 | − | 0.294514i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.09982 | − | 0.560386i | 0.0541186 | − | 0.0275748i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.4184 | + | 17.1738i | −0.756861 | + | 0.843029i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.452003 | + | 0.452003i | −0.0221347 | + | 0.0221347i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.67384i | 0.0817724i | 0.999164 | + | 0.0408862i | \(0.0130181\pi\) | ||||
−0.999164 | + | 0.0408862i | \(0.986982\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.2255 | + | 11.7885i | 0.790783 | + | 0.574538i | 0.908196 | − | 0.418545i | \(-0.137460\pi\) |
−0.117412 | + | 0.993083i | \(0.537460\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.96457 | − | 13.6687i | −0.338629 | − | 0.664597i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 35.3209 | + | 13.4413i | 1.71332 | + | 0.652000i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.71344 | + | 5.32543i | −0.131313 | + | 0.257716i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.0509236 | − | 0.828790i | 0.00245861 | − | 0.0400143i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.9561 | + | 7.13397i | −1.05759 | + | 0.343631i | −0.785642 | − | 0.618681i | \(-0.787667\pi\) |
−0.271946 | + | 0.962312i | \(0.587667\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.78393 | + | 11.2633i | −0.0857301 | + | 0.541278i | 0.907021 | + | 0.421086i | \(0.138351\pi\) |
−0.992751 | + | 0.120192i | \(0.961649\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.36001 | + | 14.3406i | −0.304939 | + | 0.687579i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 47.7441 | − | 7.56193i | 2.28391 | − | 0.361736i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.1936 | −1.05924 | −0.529621 | − | 0.848235i | \(-0.677666\pi\) | ||||
−0.529621 | + | 0.848235i | \(0.677666\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −11.1029 | −0.528708 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.1124 | − | 2.39357i | 0.718011 | − | 0.113722i | 0.213271 | − | 0.976993i | \(-0.431588\pi\) |
0.504740 | + | 0.863271i | \(0.331588\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.5769 | − | 32.6229i | −0.596204 | − | 1.54647i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.489307 | − | 3.08936i | 0.0231434 | − | 0.146122i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.5971 | − | 4.74290i | 0.688881 | − | 0.223831i | 0.0564019 | − | 0.998408i | \(-0.482037\pi\) |
0.632480 | + | 0.774577i | \(0.282037\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.74114 | + | 24.7091i | −0.458693 | + | 1.16350i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.59084 | + | 3.12221i | −0.0747444 | + | 0.146694i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.936925 | + | 0.249596i | 0.0439237 | + | 0.0117013i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.5633 | − | 22.6942i | −0.540906 | − | 1.06159i | −0.986100 | − | 0.166154i | \(-0.946865\pi\) |
0.445193 | − | 0.895434i | \(-0.353135\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −27.3162 | − | 19.8464i | −1.27501 | − | 0.926349i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 24.4297i | − | 1.13780i | −0.822405 | − | 0.568902i | \(-0.807368\pi\) | ||
0.822405 | − | 0.568902i | \(-0.192632\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.14682 | − | 3.14682i | 0.146245 | − | 0.146245i | −0.630193 | − | 0.776438i | \(-0.717024\pi\) |
0.776438 | + | 0.630193i | \(0.217024\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.60532 | − | 3.23681i | −0.167193 | − | 0.150104i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13.7387 | + | 7.00019i | −0.635749 | + | 0.323930i | −0.741991 | − | 0.670410i | \(-0.766118\pi\) |
0.106242 | + | 0.994340i | \(0.466118\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.6874 | + | 10.6710i | −0.678203 | + | 0.492743i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.68266 | − | 8.25636i | −0.123610 | − | 0.380433i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.6074 | − | 6.25223i | −0.487729 | − | 0.287478i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 28.5074 | − | 3.07966i | 1.30801 | − | 0.141304i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.87297 | − | 0.296649i | −0.0857573 | − | 0.0135826i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.40471 | + | 25.8670i | −0.384021 | + | 1.18189i | 0.553167 | + | 0.833070i | \(0.313419\pi\) |
−0.937188 | + | 0.348824i | \(0.886581\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.375048 | − | 0.516209i | 0.0171007 | − | 0.0235371i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.37345 | − | 7.37345i | −0.335504 | − | 0.335504i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.95850 | − | 18.8968i | 0.0889311 | − | 0.858061i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.40221 | − | 27.7944i | −0.199483 | − | 1.25949i | −0.860631 | − | 0.509230i | \(-0.829930\pi\) |
0.661148 | − | 0.750256i | \(-0.270070\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.10654 | − | 2.30905i | −0.321369 | − | 0.104419i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.9941 | + | 15.1321i | 0.496156 | + | 0.682901i | 0.981509 | − | 0.191418i | \(-0.0613087\pi\) |
−0.485352 | + | 0.874319i | \(0.661309\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 55.9060 | + | 28.4855i | 2.51788 | + | 1.28292i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 10.0673 | − | 13.6384i | 0.452490 | − | 0.613000i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.08446 | − | 3.10019i | −0.272925 | − | 0.139062i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.0412 | + | 16.5732i | 0.539036 | + | 0.741920i | 0.988474 | − | 0.151392i | \(-0.0483755\pi\) |
−0.449437 | + | 0.893312i | \(0.648376\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.47823 | + | 2.42982i | 0.334103 | + | 0.108557i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.71229 | − | 36.0660i | −0.254698 | − | 1.60810i | −0.700961 | − | 0.713200i | \(-0.747245\pi\) |
0.446263 | − | 0.894902i | \(-0.352755\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.01171 | − | 7.31915i | 0.401016 | − | 0.325698i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.71636 | + | 7.71636i | 0.342695 | + | 0.342695i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.397850 | − | 0.547594i | 0.0176344 | − | 0.0242717i | −0.800109 | − | 0.599855i | \(-0.795225\pi\) |
0.817743 | + | 0.575583i | \(0.195225\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.91009 | + | 5.87866i | −0.0844975 | + | 0.260057i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −25.3023 | − | 4.00748i | −1.11712 | − | 0.176935i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.49639 | + | 11.6616i | 0.110004 | + | 0.513872i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.87025 | + | 20.4158i | 0.390113 | + | 0.897885i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.517451 | − | 1.59255i | −0.0227136 | − | 0.0699052i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.2842 | − | 9.65151i | 0.581990 | − | 0.422840i | −0.257451 | − | 0.966291i | \(-0.582883\pi\) |
0.839441 | + | 0.543451i | \(0.182883\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.3641 | − | 9.86649i | 0.846732 | − | 0.431431i | 0.0238985 | − | 0.999714i | \(-0.492392\pi\) |
0.822833 | + | 0.568283i | \(0.192392\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.15208 | − | 4.58461i | −0.181211 | − | 0.200089i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13.7028 | + | 13.7028i | −0.596904 | + | 0.596904i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 48.0535i | − | 2.08928i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.55941 | − | 1.13297i | −0.0676724 | − | 0.0491669i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.07700 | + | 2.11374i | 0.0466502 | + | 0.0915562i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −24.3212 | + | 14.0888i | −1.05150 | + | 0.609111i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.19103 | + | 6.26275i | −0.137703 | + | 0.270258i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 16.0799 | + | 0.988006i | 0.692612 | + | 0.0425564i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.8196 | + | 9.68896i | −1.28204 | + | 0.416561i | −0.869299 | − | 0.494286i | \(-0.835429\pi\) |
−0.412744 | + | 0.910847i | \(0.635429\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.70411 | + | 10.7594i | −0.0731305 | + | 0.461728i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 34.4456 | − | 13.2796i | 1.47549 | − | 0.568837i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −37.7111 | + | 5.97285i | −1.61241 | + | 0.255381i | −0.896576 | − | 0.442890i | \(-0.853953\pi\) |
−0.715834 | + | 0.698270i | \(0.753953\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.33329 | 0.398335 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 47.6052 | 2.02805 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.09688 | − | 0.648882i | 0.174217 | − | 0.0275933i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.79794 | + | 1.46420i | −0.161214 | + | 0.0621518i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.58246 | + | 28.9325i | −0.194165 | + | 1.22591i | 0.677395 | + | 0.735620i | \(0.263109\pi\) |
−0.871560 | + | 0.490289i | \(0.836891\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.04595 | + | 0.339850i | −0.0442390 | + | 0.0143741i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16.3440 | + | 13.4806i | 0.690044 | + | 0.569152i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.9534 | + | 31.3102i | −0.672354 | + | 1.31957i | 0.262636 | + | 0.964895i | \(0.415408\pi\) |
−0.934990 | + | 0.354674i | \(0.884592\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.23508 | + | 4.19114i | −0.304382 | + | 0.176323i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.04801 | − | 4.01944i | −0.0860082 | − | 0.168801i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.41044 | + | 6.11055i | 0.352584 | + | 0.256167i | 0.749952 | − | 0.661492i | \(-0.230076\pi\) |
−0.397368 | + | 0.917659i | \(0.630076\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 44.5845i | − | 1.86580i | −0.360131 | − | 0.932902i | \(-0.617268\pi\) | ||
0.360131 | − | 0.932902i | \(-0.382732\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.6692 | + | 13.6692i | −0.571039 | + | 0.571039i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.08401 | − | 42.0951i | 0.0869093 | − | 1.75549i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.90672 | − | 1.48105i | 0.121008 | − | 0.0616569i | −0.392438 | − | 0.919778i | \(-0.628368\pi\) |
0.513447 | + | 0.858121i | \(0.328368\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.16214 | + | 0.844342i | −0.0482968 | + | 0.0350897i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.66867 | − | 14.3687i | −0.193689 | − | 0.596114i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.68616 | + | 0.596297i | 0.111250 | + | 0.0246961i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.316941 | − | 1.48055i | −0.0131039 | − | 0.0612134i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.94770 | − | 1.57556i | −0.410585 | − | 0.0650303i | −0.0522747 | − | 0.998633i | \(-0.516647\pi\) |
−0.358311 | + | 0.933602i | \(0.616647\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.54344 | + | 13.9833i | −0.187209 | + | 0.576170i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.50283 | − | 10.3268i | 0.308625 | − | 0.424786i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.2434 | − | 24.2434i | −0.995558 | − | 0.995558i | 0.00443249 | − | 0.999990i | \(-0.498589\pi\) |
−0.999990 | + | 0.00443249i | \(0.998589\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −19.2033 | + | 15.5966i | −0.787258 | + | 0.639397i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.06882 | + | 6.74826i | 0.0437439 | + | 0.276188i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 29.0987 | + | 9.45474i | 1.18894 | + | 0.386310i | 0.835681 | − | 0.549215i | \(-0.185073\pi\) |
0.353260 | + | 0.935525i | \(0.385073\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.3964 | − | 29.4496i | −0.872778 | − | 1.20128i | −0.978369 | − | 0.206866i | \(-0.933674\pi\) |
0.105592 | − | 0.994410i | \(-0.466326\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 25.2598 | + | 12.8705i | 1.02866 | + | 0.524128i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15.7938 | + | 18.8562i | −0.642108 | + | 0.766614i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −33.0711 | − | 16.8506i | −1.34231 | − | 0.683943i | −0.372555 | − | 0.928010i | \(-0.621518\pi\) |
−0.969758 | + | 0.244067i | \(0.921518\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.03614 | − | 8.30804i | −0.244597 | − | 0.336659i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.89089 | + | 0.614387i | 0.0764972 | + | 0.0248555i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.897929 | + | 5.66930i | 0.0362670 | + | 0.228981i | 0.999164 | − | 0.0408895i | \(-0.0130192\pi\) |
−0.962897 | + | 0.269870i | \(0.913019\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.56011 | − | 15.0529i | 0.0629098 | − | 0.606992i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.2646 | + | 17.2646i | 0.695048 | + | 0.695048i | 0.963338 | − | 0.268290i | \(-0.0864586\pi\) |
−0.268290 | + | 0.963338i | \(0.586459\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.30713 | + | 7.30464i | −0.213311 | + | 0.293598i | −0.902243 | − | 0.431229i | \(-0.858080\pi\) |
0.688931 | + | 0.724827i | \(0.258080\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11.6361 | + | 35.8122i | −0.466940 | + | 1.43710i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 22.6055 | + | 3.58037i | 0.905672 | + | 0.143444i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.46931 | − | 24.8778i | 0.0987724 | − | 0.995110i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 15.6922 | + | 3.48348i | 0.626686 | + | 0.139117i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.03083 | + | 15.4833i | 0.200593 | + | 0.617360i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.4585 | + | 10.5047i | −0.575585 | + | 0.418187i | −0.837130 | − | 0.547004i | \(-0.815768\pi\) |
0.261545 | + | 0.965191i | \(0.415768\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.9081 | + | 7.59608i | −0.592545 | + | 0.301917i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 13.8850 | + | 12.4658i | 0.551010 | + | 0.494690i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.01749 | − | 1.01749i | 0.0403146 | − | 0.0403146i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.6636i | 0.421844i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.3343 | − | 8.96143i | −0.487177 | − | 0.353955i | 0.316920 | − | 0.948452i | \(-0.397351\pi\) |
−0.804098 | + | 0.594497i | \(0.797351\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.80244 | − | 9.42531i | −0.189390 | − | 0.371698i | 0.776714 | − | 0.629854i | \(-0.216885\pi\) |
−0.966103 | + | 0.258156i | \(0.916885\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.77932 | + | 1.80601i | 0.266935 | + | 0.0711115i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.99887 | − | 3.92300i | 0.0785836 | − | 0.154229i | −0.848371 | − | 0.529402i | \(-0.822417\pi\) |
0.926955 | + | 0.375172i | \(0.122417\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.15762 | + | 1.77962i | 0.0846941 | + | 0.0698562i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.01644 | − | 0.980100i | 0.118224 | − | 0.0384131i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.30527 | + | 33.4961i | −0.207611 | + | 1.31081i | 0.635096 | + | 0.772433i | \(0.280961\pi\) |
−0.842707 | + | 0.538372i | \(0.819039\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.50937 | + | 22.0722i | 0.332488 | + | 0.862431i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.53351 | − | 1.50996i | 0.371938 | − | 0.0589091i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.3584 | 0.870962 | 0.435481 | − | 0.900198i | \(-0.356578\pi\) | ||||
0.435481 | + | 0.900198i | \(0.356578\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.3645 | 0.753194 | 0.376597 | − | 0.926377i | \(-0.377094\pi\) | ||||
0.376597 | + | 0.926377i | \(0.377094\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.86903 | − | 0.296025i | 0.0725871 | − | 0.0114967i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.60956 | + | 17.1581i | −0.295086 | + | 0.665362i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.9464 | − | 69.1131i | 0.423848 | − | 2.67607i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −18.9078 | + | 6.14351i | −0.731017 | + | 0.237522i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.5171 | − | 0.830537i | −0.521823 | − | 0.0320625i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.20467 | − | 4.32690i | 0.0849837 | − | 0.166790i | −0.844603 | − | 0.535393i | \(-0.820164\pi\) |
0.929587 | + | 0.368603i | \(0.120164\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7.94409 | + | 20.8754i | −0.305768 | + | 0.803493i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.59274 | + | 10.9764i | 0.214946 | + | 0.421856i | 0.973153 | − | 0.230158i | \(-0.0739243\pi\) |
−0.758207 | + | 0.652014i | \(0.773924\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.0612 | + | 7.30988i | 0.386113 | + | 0.280527i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 15.2678i | − | 0.585063i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.62361 | − | 3.62361i | 0.138654 | − | 0.138654i | −0.634373 | − | 0.773027i | \(-0.718742\pi\) |
0.773027 | + | 0.634373i | \(0.218742\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17.9548 | + | 19.9989i | −0.686016 | + | 0.764118i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.757800 | + | 0.386118i | −0.0289119 | + | 0.0147313i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.198829 | − | 0.144458i | 0.00757479 | − | 0.00550340i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.92606 | − | 12.0832i | −0.149355 | − | 0.459666i | 0.848191 | − | 0.529691i | \(-0.177692\pi\) |
−0.997545 | + | 0.0700250i | \(0.977692\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.42194 | + | 10.1775i | 0.167976 | + | 0.386613i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.919084 | − | 1.41976i | 0.0348629 | − | 0.0538545i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −59.7833 | − | 9.46875i | −2.26445 | − | 0.358654i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.49268 | − | 4.59401i | 0.0564585 | − | 0.173761i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.86123 | − | 5.31453i | 0.145837 | − | 0.200727i | −0.729849 | − | 0.683608i | \(-0.760410\pi\) |
0.875686 | + | 0.482881i | \(0.160410\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.73413 | + | 8.73413i | 0.329414 | + | 0.329414i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.99607 | − | 9.84517i | −0.301149 | − | 0.370790i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.18886 | + | 7.50614i | 0.0447115 | + | 0.282297i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −31.3578 | − | 10.1888i | −1.17767 | − | 0.382648i | −0.346168 | − | 0.938172i | \(-0.612517\pi\) |
−0.831500 | + | 0.555525i | \(0.812517\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.80726 | − | 5.24025i | −0.142783 | − | 0.196525i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 19.2561 | + | 9.81148i | 0.721147 | + | 0.367443i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.327266 | + | 2.17245i | 0.0122391 | + | 0.0812449i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.5793 | + | 5.39044i | 0.395093 | + | 0.201310i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27.5659 | − | 37.9411i | −1.02803 | − | 1.41497i | −0.906415 | − | 0.422389i | \(-0.861192\pi\) |
−0.121618 | − | 0.992577i | \(-0.538808\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.42467 | − | 2.41242i | −0.276509 | − | 0.0898433i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.24612 | − | 14.1814i | −0.0835341 | − | 0.527414i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.51222 | − | 40.6244i | 0.316136 | − | 1.50875i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.60329 | + | 6.60329i | 0.244902 | + | 0.244902i | 0.818875 | − | 0.573972i | \(-0.194598\pi\) |
−0.573972 | + | 0.818875i | \(0.694598\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.51668 | − | 3.46392i | 0.0932104 | − | 0.128293i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.67114 | − | 26.6870i | 0.320714 | − | 0.987056i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.19333 | − | 0.822542i | −0.191820 | − | 0.0303813i | 0.0597852 | − | 0.998211i | \(-0.480958\pi\) |
−0.251605 | + | 0.967830i | \(0.580958\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8.97610 | + | 1.92150i | −0.331088 | + | 0.0708757i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −35.4377 | − | 20.8878i | −1.30537 | − | 0.769411i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.7995 | − | 33.2374i | −0.397266 | − | 1.22266i | −0.927183 | − | 0.374609i | \(-0.877777\pi\) |
0.529917 | − | 0.848050i | \(-0.322223\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.16153 | − | 0.843902i | 0.0426699 | − | 0.0310015i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −46.5352 | + | 23.7109i | −1.70721 | + | 0.869868i | −0.723453 | + | 0.690374i | \(0.757446\pi\) |
−0.983759 | + | 0.179495i | \(0.942554\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.445074 | + | 8.26379i | 0.0163063 | + | 0.302762i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −16.6823 | + | 16.6823i | −0.610375 | + | 0.610375i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 18.3992i | − | 0.672293i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.4792 | + | 9.06665i | 0.455372 | + | 0.330847i | 0.791713 | − | 0.610893i | \(-0.209190\pi\) |
−0.336341 | + | 0.941740i | \(0.609190\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.06101 | + | 2.08235i | 0.0386653 | + | 0.0758850i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.38663 | − | 8.95884i | 0.0868584 | − | 0.326046i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.43234 | − | 14.5868i | 0.270133 | − | 0.530166i | −0.715594 | − | 0.698516i | \(-0.753844\pi\) |
0.985727 | + | 0.168350i | \(0.0538440\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.66560 | − | 21.9809i | 0.314541 | − | 0.797855i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.4053 | + | 4.35565i | −0.485943 | + | 0.157892i | −0.541734 | − | 0.840550i | \(-0.682232\pi\) |
0.0557912 | + | 0.998442i | \(0.482232\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.78041 | + | 23.8686i | −0.136860 | + | 0.864100i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 35.3145 | + | 15.6619i | 1.27680 | + | 0.566255i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.246737 | − | 0.0390792i | 0.00890914 | − | 0.00141107i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.97963 | −0.179570 | −0.0897850 | − | 0.995961i | \(-0.528618\pi\) | ||||
−0.0897850 | + | 0.995961i | \(0.528618\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.9186 | −0.537279 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20.0917 | + | 3.18221i | −0.722647 | + | 0.114456i | −0.506914 | − | 0.861996i | \(-0.669214\pi\) |
−0.215733 | + | 0.976452i | \(0.569214\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.1204 | + | 6.37751i | 0.399455 | + | 0.229087i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.416824 | − | 2.63173i | 0.0149535 | − | 0.0944126i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −43.6761 | + | 14.1912i | −1.56486 | + | 0.508453i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.948914 | − | 15.4437i | 0.0339548 | − | 0.552620i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −16.8355 | + | 33.0416i | −0.601652 | + | 1.18081i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.5133 | + | 19.8751i | 0.410926 | + | 0.709373i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.41237 | − | 4.73454i | −0.0859917 | − | 0.168768i | 0.844006 | − | 0.536334i | \(-0.180191\pi\) |
−0.929998 | + | 0.367566i | \(0.880191\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.78828 | − | 2.02580i | −0.0992654 | − | 0.0721205i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 5.47342i | − | 0.194612i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.855326 | + | 0.855326i | −0.0303735 | + | 0.0303735i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.56554 | + | 0.0843173i | −0.0555239 | + | 0.00299043i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35.1948 | − | 17.9327i | 1.24667 | − | 0.635208i | 0.298933 | − | 0.954274i | \(-0.403369\pi\) |
0.947732 | + | 0.319066i | \(0.103369\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −41.0400 | + | 29.8173i | −1.45189 | + | 1.05486i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.0443 | − | 33.9909i | −0.390231 | − | 1.20101i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.9415 | + | 1.33848i | −0.491984 | + | 0.0472338i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 23.1603 | + | 14.9929i | 0.816293 | + | 0.528430i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.13865 | − | 0.338730i | −0.0752842 | − | 0.0119238i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.94301 | − | 27.5237i | 0.314419 | − | 0.967683i | −0.661573 | − | 0.749880i | \(-0.730111\pi\) |
0.975993 | − | 0.217803i | \(-0.0698890\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.60859 | + | 2.21403i | −0.0564852 | + | 0.0777453i | −0.836325 | − | 0.548234i | \(-0.815300\pi\) |
0.779840 | + | 0.625979i | \(0.215300\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.289000 | − | 0.289000i | −0.0101357 | − | 0.0101357i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19.6649 | + | 2.03811i | 0.688830 | + | 0.0713917i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.33046 | − | 21.0277i | −0.116518 | − | 0.735665i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.942634 | + | 0.306280i | 0.0329383 | + | 0.0107023i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.2748 | + | 21.0240i | 0.533096 | + | 0.733743i | 0.987598 | − | 0.157002i | \(-0.0501829\pi\) |
−0.454502 | + | 0.890745i | \(0.650183\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.58273 | − | 4.88264i | −0.334033 | − | 0.170198i | 0.278927 | − | 0.960312i | \(-0.410021\pi\) |
−0.612960 | + | 0.790114i | \(0.710021\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.77856 | − | 12.7682i | 0.201184 | − | 0.444532i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32.3953 | + | 16.5062i | 1.12649 | + | 0.573977i | 0.915021 | − | 0.403407i | \(-0.132174\pi\) |
0.211473 | + | 0.977384i | \(0.432174\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.6173 | + | 25.6245i | 0.646604 | + | 0.889974i | 0.998946 | − | 0.0458969i | \(-0.0146146\pi\) |
−0.352342 | + | 0.935871i | \(0.614615\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18.7257 | − | 6.08433i | −0.649586 | − | 0.211063i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.74340 | + | 36.2624i | 0.198997 | + | 1.25642i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −20.6934 | − | 2.14470i | −0.716125 | − | 0.0742205i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.09864 | − | 8.09864i | −0.279930 | − | 0.279930i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.75378 | − | 9.29577i | 0.233166 | − | 0.320926i | −0.676361 | − | 0.736570i | \(-0.736444\pi\) |
0.909527 | + | 0.415645i | \(0.136444\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.3335 | − | 37.9586i | 0.425293 | − | 1.30892i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 14.9427 | + | 2.36669i | 0.514654 | + | 0.0815132i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −24.2374 | − | 15.6901i | −0.833791 | − | 0.539757i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.49850 | − | 15.1333i | −0.188931 | − | 0.519987i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.90789 | − | 15.1049i | −0.168438 | − | 0.518400i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.6885 | − | 10.6718i | 0.503516 | − | 0.365826i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −33.5651 | + | 17.1023i | −1.14925 | + | 0.585571i | −0.921588 | − | 0.388170i | \(-0.873107\pi\) |
−0.227659 | + | 0.973741i | \(0.573107\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 29.2679 | − | 1.57632i | 1.00094 | − | 0.0539091i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −38.5292 | + | 38.5292i | −1.31613 | + | 1.31613i | −0.399323 | + | 0.916810i | \(0.630755\pi\) |
−0.916810 | + | 0.399323i | \(0.869245\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 13.1305i | − | 0.448007i | −0.974588 | − | 0.224004i | \(-0.928087\pi\) | ||
0.974588 | − | 0.224004i | \(-0.0719127\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.01458 | + | 5.82293i | 0.273136 | + | 0.198445i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.96508 | − | 5.81929i | −0.100932 | − | 0.198091i | 0.835018 | − | 0.550222i | \(-0.185457\pi\) |
−0.935951 | + | 0.352131i | \(0.885457\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.22076 | + | 3.83366i | 0.0755082 | + | 0.130348i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −15.3970 | + | 30.2183i | −0.522909 | + | 1.02627i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.04763 | + | 7.92809i | 0.171229 | + | 0.268942i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.49436 | + | 1.13539i | −0.118402 | + | 0.0384711i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.03798 | − | 19.1810i | 0.102820 | − | 0.649180i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 13.2814 | + | 9.56171i | 0.448993 | + | 0.323245i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.2502 | − | 1.62347i | 0.346125 | − | 0.0548208i | 0.0190480 | − | 0.999819i | \(-0.493936\pi\) |
0.327077 | + | 0.944998i | \(0.393936\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −22.3784 | −0.754804 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.81394 | 0.0948039 | 0.0474020 | − | 0.998876i | \(-0.484906\pi\) | ||||
0.0474020 | + | 0.998876i | \(0.484906\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −39.1108 | + | 6.19453i | −1.31618 | + | 0.208463i | −0.774742 | − | 0.632277i | \(-0.782120\pi\) |
−0.541439 | + | 0.840740i | \(0.682120\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.45678 | − | 0.646075i | −0.0489690 | − | 0.0217176i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.24874 | + | 33.1393i | −0.176236 | + | 1.11271i | 0.727970 | + | 0.685609i | \(0.240464\pi\) |
−0.904205 | + | 0.427098i | \(0.859536\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.6171 | + | 3.77461i | −0.389624 | + | 0.126597i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.50386 | − | 7.88532i | 0.217888 | − | 0.264168i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −17.4732 | + | 34.2932i | −0.584719 | + | 1.14758i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.78728 | − | 17.9703i | 0.160021 | − | 0.600681i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.958089 | − | 1.88036i | −0.0319897 | − | 0.0627832i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.2187 | + | 12.5101i | 0.574275 | + | 0.417236i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.27064i | 0.208905i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.24745 | + | 3.24745i | −0.108068 | + | 0.108068i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.55007 | − | 28.7804i | −0.0515259 | − | 0.956693i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35.7325 | + | 18.2066i | −1.18648 | + | 0.604541i | −0.931972 | − | 0.362530i | \(-0.881913\pi\) |
−0.254507 | + | 0.967071i | \(0.581913\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.60097 | − | 6.97551i | 0.318444 | − | 0.231363i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.63301 | − | 23.4920i | −0.252893 | − | 0.778325i | −0.994237 | − | 0.107200i | \(-0.965811\pi\) |
0.741344 | − | 0.671125i | \(-0.234189\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.6450 | − | 22.6760i | 0.848727 | − | 0.750467i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.54548 | − | 1.61525i | 0.249446 | − | 0.0533986i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −15.2946 | − | 2.42242i | −0.505071 | − | 0.0799955i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.4328 | − | 44.4197i | 0.476095 | − | 1.46527i | −0.368380 | − | 0.929675i | \(-0.620088\pi\) |
0.844475 | − | 0.535594i | \(-0.179912\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.12318 | − | 9.80421i | 0.234717 | − | 0.323060i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.977236 | − | 0.977236i | −0.0321661 | − | 0.0321661i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.01510 | − | 5.89162i | 0.296415 | − | 0.193715i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.90706 | + | 12.0407i | 0.0626361 | + | 0.395469i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 44.1182 | + | 14.3349i | 1.44747 | + | 0.470312i | 0.924218 | − | 0.381864i | \(-0.124718\pi\) |
0.523254 | + | 0.852177i | \(0.324718\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.3732 | + | 22.5357i | 0.536609 | + | 0.738578i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −18.6898 | − | 9.52293i | −0.611877 | − | 0.311767i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −49.7512 | − | 25.8251i | −1.62704 | − | 0.844571i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −50.0611 | − | 25.5074i | −1.63542 | − | 0.833290i | −0.998029 | − | 0.0627527i | \(-0.980012\pi\) |
−0.637395 | − | 0.770537i | \(-0.719988\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.16947 | − | 1.60963i | −0.0381641 | − | 0.0525284i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −34.9147 | − | 11.3445i | −1.13819 | − | 0.369819i | −0.321506 | − | 0.946908i | \(-0.604189\pi\) |
−0.816682 | + | 0.577088i | \(0.804189\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.5598 | + | 66.6719i | 0.343874 | + | 2.17114i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −9.21788 | − | 11.3495i | −0.299858 | − | 0.369200i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.8812 | − | 12.8812i | −0.418582 | − | 0.418582i | 0.466133 | − | 0.884715i | \(-0.345647\pi\) |
−0.884715 | + | 0.466133i | \(0.845647\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.735299 | + | 1.01205i | −0.0238688 | + | 0.0328526i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.77645 | − | 14.7004i | 0.154887 | − | 0.476693i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.630156 | − | 0.0998069i | −0.0204127 | − | 0.00323306i | 0.146220 | − | 0.989252i | \(-0.453289\pi\) |
−0.166632 | + | 0.986019i | \(0.553289\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 27.7944 | − | 42.9355i | 0.899406 | − | 1.38936i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11.8153 | − | 20.0456i | 0.381934 | − | 0.647981i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.43666 | − | 16.7323i | −0.175559 | − | 0.540315i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.7615 | − | 14.3576i | 0.637469 | − | 0.463148i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −25.6001 | + | 13.0439i | −0.824951 | + | 0.420334i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.53905 | − | 2.82812i | 0.0817349 | − | 0.0910403i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.3036 | − | 10.3036i | 0.331340 | − | 0.331340i | −0.521755 | − | 0.853095i | \(-0.674722\pi\) |
0.853095 | + | 0.521755i | \(0.174722\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 36.6322i | 1.17680i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −31.2434 | − | 22.6996i | −1.00265 | − | 0.728466i | −0.0399933 | − | 0.999200i | \(-0.512734\pi\) |
−0.962654 | + | 0.270734i | \(0.912734\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.502626 | + | 0.986459i | 0.0161134 | + | 0.0316244i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.512461 | − | 1.14210i | −0.0164119 | − | 0.0365765i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.7547 | + | 42.6959i | −0.695993 | + | 1.36596i | 0.224217 | + | 0.974539i | \(0.428018\pi\) |
−0.920210 | + | 0.391424i | \(0.871982\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.9704 | + | 50.2108i | 0.414536 | + | 1.60474i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 35.8900 | − | 11.6614i | 1.14588 | − | 0.372319i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.77684 | + | 11.2185i | −0.0566725 | + | 0.357816i | 0.943013 | + | 0.332755i | \(0.107978\pi\) |
−0.999686 | + | 0.0250612i | \(0.992022\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.6920 | + | 30.8728i | −0.436262 | + | 0.983688i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.20035 | − | 1.29881i | 0.261020 | − | 0.0413415i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −31.2937 | −0.995081 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.0668 | −1.01863 | −0.509317 | − | 0.860579i | \(-0.670102\pi\) | ||||
−0.509317 | + | 0.860579i | \(0.670102\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11.4185 | − | 1.80852i | 0.362356 | − | 0.0573915i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.50270 | − | 16.8671i | −0.206149 | − | 0.534724i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.34985 | − | 27.4639i | 0.137761 | − | 0.869790i | −0.817908 | − | 0.575348i | \(-0.804866\pi\) |
0.955670 | − | 0.294441i | \(-0.0951335\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9.15095 | + | 2.97332i | −0.289523 | + | 0.0940718i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 880.2.cm.b.17.5 | 48 | ||
4.3 | odd | 2 | 220.2.u.a.17.2 | yes | 48 | ||
5.3 | odd | 4 | inner | 880.2.cm.b.193.5 | 48 | ||
11.2 | odd | 10 | inner | 880.2.cm.b.497.5 | 48 | ||
20.3 | even | 4 | 220.2.u.a.193.2 | yes | 48 | ||
44.35 | even | 10 | 220.2.u.a.57.2 | yes | 48 | ||
55.13 | even | 20 | inner | 880.2.cm.b.673.5 | 48 | ||
220.123 | odd | 20 | 220.2.u.a.13.2 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
220.2.u.a.13.2 | ✓ | 48 | 220.123 | odd | 20 | ||
220.2.u.a.17.2 | yes | 48 | 4.3 | odd | 2 | ||
220.2.u.a.57.2 | yes | 48 | 44.35 | even | 10 | ||
220.2.u.a.193.2 | yes | 48 | 20.3 | even | 4 | ||
880.2.cm.b.17.5 | 48 | 1.1 | even | 1 | trivial | ||
880.2.cm.b.193.5 | 48 | 5.3 | odd | 4 | inner | ||
880.2.cm.b.497.5 | 48 | 11.2 | odd | 10 | inner | ||
880.2.cm.b.673.5 | 48 | 55.13 | even | 20 | inner |